Apart from symbol and frame synchronization, digital receiver systems for wireless transmission systems require the estimation and correction of a phase offset and of a frequency offset for the correct and power-efficient detection of the transmitted symbols.
For the digital frequency offset estimation, heuristic methods are used which utilize known signal characteristics or characteristics of signals derived from the received signal, and methods which are based on the so-called maximum likelihood principle. In these methods, a basic distinction is made between data-aided and non-data-aided methods and clock-aided and non-clock-aided methods. Furthermore, estimating methods with or without feedback (feedback or feedforward) are known. All of these methods are based on the use of the complex envelope of the received signal which is analog/digital-converted with adequate resolution.
From the text book “Synchronization Techniques For Digital Receivers”, U. Mengali and A. N. D'Andrea, Plenum Press, New York, 1997, a heuristic method is known which works in accordance with the so-called “delay-and-multiply” method. In this method, an intermediate signal is generated from the product of a sampled input signal in complex form and a conjugate-complex input signal, displaced in time with respect to the former. Evaluation of this intermediate signal over an observation interval comprising N received symbols results in the required frequency offset. In the method, a differential demodulator is used as essential component. The disadvantageous factor in such a method is that an analog/digital converter operating with adequate resolution is necessary for sampling the input signal. In addition, gain control of the analog input signal is required apart from the linearity of the analog preprocessing.
From PCT Publication WO 01/45339 A2, a further method for estimating a frequency offset is known which is based on the above-mentioned method. In this document, an improved estimation of the frequency offset in CPFSK-modulated (continuous phase frequency shift keying) input signals is proposed by taking into consideration an additional delay parameter D. This method also exhibits the above-mentioned disadvantages.
For short-range wireless transmission systems such as are provided, for example, in the Bluetooth standard, so-called limiter-discriminator receiver concepts are known in which the received analog signal (possibly down-converted into a suitable intermediate frequency range) is converted into a hard-limited value-discrete 1-bit signal by using a limiter. The further signal processing is only based on this 1-bit signal. This concept is very interesting from points of view of economy since it is possible to dispense with an (expensive) analog/digital converter for quantizing the received analog signal. However, the procedures for frequency-offset estimation, explained above, cannot be used since there are no samples of the received analog signal which are obtained with adequate resolution.
From the text book “Irreguläre Abtastung (irregular sampling)”, A. Neubauer, Springer-Verlag 2003, as described in chapter 8.2.2, pages 402 to 404, and algorithm 7.11, pages 375 to 377, a method is known which enables the instantaneous frequency of a modulation signal to be reconstructed by only evaluating the zero cross-overs of the modulated bandpass signal. For this purpose, the times of the zero cross-overs of the modulated bandpass signal are first determined. From the values of two adjacent times, the local mean value of the instantaneous frequency of the modulation signal between these adjacent times can be determined when the carrier frequency is known. A reconstruction of the required instantaneous frequency can then be performed via a multiplicity of local mean values with the aid of a Fourier series expansion of the instantaneous frequency. In this context, a recursive method for determining the corresponding Fourier coefficients is proposed. The Fourier series expansion of the instantaneous frequency then results in the required variation with time of the instantaneous frequency.